More on Graph Rewriting With Contextual Refinement

In grgen, a graph rewrite generator tool, rules have the outstanding feature that variables in their pattern and replacement graphs may be refined with meta-rules based on contextual hyperedge replacement grammars. A refined rule may delete, copy, and transform subgraphs of unbounded size and of variable shape. In this paper, we show that rules with contextual refinement can be transformed to standard graph rewrite rules that perform the refinement incrementally, and are applied according to a strategy called residual rewriting. With this transformation, it is possible to state precisely whether refinements can be determined in finitely many steps or not, and whether refinements are unique for every form of refined pattern or not.